In this paper we develop an iterative numerical method based on Bernstein splines for solving two-point boundary problems associated to differential equations of fractional order $\alpha\in\left( 0,1\right) $. The convergence the is proved by providing error estimate and it tested a example.

In this paper, the optimal conditions for fractional optimal control problems (FOCPs) were derived in which the fractional differential operators defined in terms of Caputo sense and reduces this problem to a system of fractional differential equations (FDEs) that is called twopoint boundary value (TPBV) problem. An approximate solution of this problem is constructed by using the Legendre-Gauss...

Fractional differential equations have extensively used in physics, chemistry as well as engineering fields. Therefore, approximating the solution of differential equations of fractional order is necessary. Consequently, it is essential to approximate the solution of differential equations of fractional order. The piecewise quadratic polynomial function based method has been presented in this p...

in this paper, we use a third degree b-spline function to construct an approximate solution forthird order linear and nonlinear boundary value problems coupled with the least square method. severalexamples are given to illustrate the efficiency of the proposed technique.

Abstract: This paper is motivated from some recent papers treating the boundary value problems for impulsive fractional differential equations. We first give some notations, recall some concepts and preparation results. Second, we establish a general framework to find the solutions for impulsive fractional boundary value problems, which will provide an effective way to deal with such problems. ...